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Theorem 2exsb 1885
 Description: An equivalent expression for double existence. (Contributed by NM, 2-Feb-2005.)
Assertion
Ref Expression
2exsb
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem 2exsb
StepHypRef Expression
1 exsb 1884 . . . 4
21exbii 1496 . . 3
3 excom 1554 . . 3
42, 3bitri 173 . 2
5 exsb 1884 . . . 4
6 impexp 250 . . . . . . . 8
76albii 1359 . . . . . . 7
8 19.21v 1753 . . . . . . 7
97, 8bitr2i 174 . . . . . 6
109albii 1359 . . . . 5
1110exbii 1496 . . . 4
125, 11bitri 173 . . 3
1312exbii 1496 . 2
14 excom 1554 . 2
154, 13, 143bitri 195 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241  wex 1381 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-sb 1646 This theorem is referenced by: (None)
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